Looks like this game is broken, after receiving the FTL drive and "recalibrating", nothing happens (as in no new main quests appear)
The quest menu tells me to upgrade my ship... but nothing happens if I upgrade my ship either.
Sorry I never got back to you on this! A while ago I removed the "Stories" App from the tablet, which was the source of new quests besides RNG quests. This is not broken, the game has just changed direction, after you recalibrate it changes RNG quests over to the new quest system which works much better and has a better variety of RNG quests. I wanted to focus more on exploration and less on Quests as I'm not a great story teller, hope this clears things up! :)
Edit 2/24/23: The app is now usable again, but only Steam has the update currently.